University:
Santa Fe College
Course:
PHY 2004 | Applied Physics 1
Academic year:

2024
Views:

443

Pages:

5
Author:

Jabin F.

#Conservation of linear momentum: If Lart is invariant under translation of origin of co-ardinate system in certain direction then linear momeritum is conserved in that direction. x Xx In general when origin is translated them t lincer momention in the dietetion of translation is consed. ie. xpx + β pytYp₂ is conserved. Example if L=m(x²+y²) + (4x (94) then Cobx 7 G by or ( by 7 (b, is conserved. Prooff let us translete origin ro that I doesnat change = Y L= (+) + (C, x' + (५). = ½ m (x² + y²) + ( ( (1x+6)² + (y-1)²) - L = ½ m (x² + y²) + ( (1x+6)² + (y-1)²) - L => (bx-by-by is conserved check if it is really conserved then d/dt (bx-by) = (bx-by) = (9x-by) = (9x-by) - (9x-by) = 0 .. quantity (bx-by) is conserved. #Related Statements: → Homogeneity of space leads to conservation of linear momentum. → Translational invariance of Lagrangian leads to conservation of linear momentum. → If Lagrangian of a system, L = ½m(x² + y²) + (x² + y² - 5x²) which of the following is conserved? a) ½m(x² + y²) b) ½m(x² + y²) + 5x² c) ½m(x² + y²) + 5pz d) ½m(x² + y²) + 5p₂ Solution: a) x² + y² b) x² + y² - 5x² c) x² + y² + 5pz d) x² + y² + 5p₂